Controlled phase flip (CPF) gate or its equivalent controlled-NOT (CNOT) gate is the most quintessential universal quantum gate [1]}. CNOT gates together with single-qubit rotations are sufficient to implement any quantum computation [2]}. Nowadays, CNOT gate has been experimentally demonstrated in several physical systems [3]}, [4]}, [5]}.
The KLM scheme [6]} is served as a stepping stone for implementing CPF gate with a sheer number of linear optics, large and good quantum memory, and giant interferometer phase stable. Various improved works were later proposed both in theory and experiment [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}, [19]}, [20]}, [21]}, [22]}.
So far, it has been demonstrated that CPF gate can be completed with a success probability of 1/9, which is the existing maximum value achievable without ancillary photons [13]}, [14]}, [15]}, [16]}, [17]}, [18]},
and the success probability can be improved to 1/8 via two additional independent single photons [19]}, [20]}.
The current existing highest success probability of 1/4 for a CNOT gate has been achieved assisted by a necessary entangled photon pair [8]}, [9]}, [10]}, [11]}, [12]}. Deterministic generation of entangled photon pairs based on spontaneous parametric down-conversion remains a key technical obstacle in experiments due to multi-photon emissions and probabilistic properties [36]}.
